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A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

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Abstract

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra \({\mathbb{H}_2}\). The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.

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Authors and Affiliations

  1. Laboratorio de Optica Cuántica, Departamento de Física, Universidad Autónoma Metropolitana-I, 09340, México, D. F., México

    Manuel Fernández-Guasti

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, 09340, México, D. F., México

    Felipe Zaldívar

Authors
  1. Manuel Fernández-Guasti
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  2. Felipe Zaldívar
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Correspondence to Manuel Fernández-Guasti.

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Fernández-Guasti, M., Zaldívar, F. A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions. Adv. Appl. Clifford Algebras 23, 639–656 (2013). https://doi.org/10.1007/s00006-013-0386-4

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  • DOI: https://doi.org/10.1007/s00006-013-0386-4

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